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Financial Modeling & the Crisis
Terry MarshQuantal International Inc.
19th Annual Conference of the PBFEAM
Friday, July 8 , 2011Taipei
Joint Work, Background Papers
Work is with Paul Pfleiderer
http://www.quantal.com/Research
Outline
MyAsset
Allocation Model
Failed!!!!
No Diversification when I needed
it!!
Black Swans!!!
25-standard deviations!!!!
Outline (cont’d.)
BASECASE
VARIATIONSCrisis Hits: Allocation Weights Change Because of
Price Declines
Specify Pre-Crisis Market Environment and Determine Optimal Allocations for Various
Clientele
Solve for Post-Crisis Market-Clearing Equilibrium and Optimal Allocations
Calculate Turnover caused by the Crisis
Pre-Crisis: Market Environment: Assumed Risk-Return Structure, Market Index Weights
Market Standard US Dev Em EquilibriumWeights Deviation Equity Equity Equity Bonds Exp Return*
US Equity 20.00% 18.00% 1.00 0.65 0.60 0.40 7.11%
Dev Equity 22.00% 20.00% 0.65 1.00 0.60 0.35 7.60%Em Equity 18.00% 30.00% 0.60 0.60 1.00 0.30 9.84%
Bonds 30.00% 10.00% 0.40 0.35 0.30 1.00 4.71%
Cash 10.00% 0.00% 3.00%**
** Borrowing Cost = 3.50%
Correlations
* Average Risk Tolerance = 0.5
Pre-Crisis: Investor Clienteles and Market-Clearing Allocations (Optimal for each Clientele)
Clientele (a) (b) (c) (d) (e) (f) (g)
Risk Tolerance 0.2 0.3 0.4 0.5 0.6 0.7 0.8
% of Total Wealth 5.00% 10.00% 20.00% 30.00% 20.00% 10.00% 5.00%
US Equity 8.36% 12.53% 16.71% 20.89% 23.26% 25.88% 29.57%
Dev Equity 9.07% 13.61% 18.14% 22.68% 25.84% 29.19% 33.36%
Em Equity 7.03% 10.55% 14.07% 17.59% 21.94% 26.18% 29.92%
Bonds 15.40% 23.11% 30.81% 38.51% 28.96% 21.72% 24.82%
Cash 60.13% 40.20% 20.27% 0.34% 0.00% -2.97% -17.69%
Total 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00%
Optimal Allocations
Total
US Equity 0.42% 1.25% 3.34% 6.27% 4.65% 2.59% 1.48% 20.00%
Dev Equity 0.45% 1.36% 3.63% 6.80% 5.17% 2.92% 1.67% 22.00%
Em Equity 0.35% 1.06% 2.81% 5.28% 4.39% 2.62% 1.50% 18.00%
Bonds 0.77% 2.31% 6.16% 11.55% 5.79% 2.17% 1.24% 30.00%
Cash 3.01% 4.02% 4.05% 0.10% 0.00% -0.30% -0.88% 10.00%
Total 5.00% 10.00% 20.00% 30.00% 20.00% 10.00% 5.00% 100.00%
% Holdings in Economy
Post-Crisis: Realized Allocations After Huge Price Changes
Clientele (a) (b) (c) (d) (e) (f) (g)
New Level of Risk Tolerance 0.1 0.2 0.3 0.4 0.5 0.6 0.7
New % of Total Wealth 6.24% 11.57% 21.32% 29.27% 18.69% 8.87% 4.05%
US Equity 5.47% 8.85% 12.80% 17.48% 20.32% 23.82% 29.83%Dev Equity 5.94% 9.60% 13.89% 18.97% 22.57% 26.87% 33.65%
Em Equity 4.60% 7.45% 10.77% 14.71% 19.17% 24.10% 30.18%
Bonds 15.12% 24.46% 35.38% 48.34% 37.94% 29.99% 37.56%
Cash 68.87% 49.65% 27.16% 0.49% 0.00% -4.79% -31.22%
Total 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00%
Allocations after 40%
Decline in Equity, 10%
Decline in Bonds and 5%
Gain In Riskless
Total
US Equity 0.34% 1.02% 2.73% 5.12% 3.80% 2.11% 1.21% 16.33%Dev Equity 0.37% 1.11% 2.96% 5.55% 4.22% 2.38% 1.36% 17.96%
Em Equity 0.29% 0.86% 2.30% 4.31% 3.58% 2.14% 1.22% 14.69%
Bonds 0.94% 2.83% 7.55% 14.15% 7.09% 2.66% 1.52% 36.74%
Cash 4.30% 5.74% 5.79% 0.14% 0.00% -0.42% -1.26% 14.29%
Total 6.24% 11.57% 21.32% 29.27% 18.69% 8.87% 4.05% 100.00%
% Holdings after 40%
Decline in Equity, 10%
Decline in Bonds and 5%
Gain In Riskless
Market Environment Before and After: Assumed Risk-Return Structure, Market Index Weights
Market Standard US Dev Em Equilibrium
Weights Deviation Equity Equity Equity Bonds Exp Return*
US Equity 20.00% 18.00% 1.00 0.65 0.60 0.40 7.11%
Dev Equity 22.00% 20.00% 0.65 1.00 0.60 0.35 7.60%
Em Equity 18.00% 30.00% 0.60 0.60 1.00 0.30 9.84%
Bonds 30.00% 10.00% 0.40 0.35 0.30 1.00 4.71%
Cash 10.00% 0.00% 3.00%**
** Borrowing Cost = 3.50%
Correlations
* Average Risk Tolerance = 0.5
BEFORE
Market Standard US Dev Em Equilibrium
Weights Deviation Equity Equity Equity Bonds Exp Return*
US Equity 16.33% 30.00% 1.00 0.75 0.70 0.50 13.53%
Dev Equity 17.96% 30.00% 0.75 1.00 0.70 0.50 13.63%
Em Equity 14.69% 40.00% 0.70 0.70 1.00 0.45 17.37%
Bonds 36.73% 15.00% 0.50 0.50 0.45 1.00 6.40%
Cash 14.29% 0.00% 1%**
** Borrowing Cost = 1.50%
Correlations
* Average Risk Tolerance = 0.385
AFTER
Optimal Allocations and TurnoverClientele (a) (b) (c) (d) (e) (f) (g)
Risk Tolerance 0.1 0.2 0.3 0.4 0.5 0.6 0.7% of Total Wealth 6.24% 11.57% 21.32% 29.27% 18.69% 8.87% 4.05%
US Equity 4.27% 8.54% 12.81% 17.08% 20.98% 25.18% 29.37%Dev Equity 4.69% 9.39% 14.08% 18.77% 23.10% 27.72% 32.34%Em Equity 3.75% 7.49% 11.24% 14.99% 19.45% 23.34% 27.23%
Bonds 10.55% 21.11% 31.66% 42.21% 41.52% 49.82% 58.13%Cash 76.74% 53.48% 30.21% 6.95% -5.05% -26.07% -47.08%Total 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00%
New Optimal Allocations
TotalUS Equity 0.27% 0.99% 2.73% 5.00% 3.92% 2.23% 1.19% 16.33%
Dev Equity 0.29% 1.09% 3.00% 5.49% 4.32% 2.46% 1.31% 17.96%Em Equity 0.23% 0.87% 2.40% 4.39% 3.64% 2.07% 1.10% 14.69%
Bonds 0.66% 2.44% 6.75% 12.35% 7.76% 4.42% 2.35% 36.73%Cash 4.79% 6.19% 6.44% 2.03% -0.94% -2.31% -1.91% 14.29%Total 6.24% 11.57% 21.32% 29.27% 18.69% 8.87% 4.05% 100.00%
New % Holdings in Economy
US Equity -1.20% -0.31% 0.01% -0.40% 0.66% 1.36% -0.45%Dev Equity -1.24% -0.22% 0.19% -0.20% 0.53% 0.85% -1.31%Em Equity -0.86% 0.05% 0.47% 0.27% 0.29% -0.76% -2.95%
Bonds -4.57% -3.35% -3.73% -6.13% 3.58% 19.83% 20.57%Cash 7.87% 3.83% 3.05% 6.46% -5.05% -21.27% -15.86%Total 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
Change in Allocations
TotalUS Equity -0.07% -0.04% 0.00% -0.12% 0.12% 0.12% -0.02% 0.00%
Dev Equity -0.08% -0.02% 0.04% -0.06% 0.10% 0.08% -0.05% 0.00%Em Equity -0.05% 0.01% 0.10% 0.08% 0.05% -0.07% -0.12% 0.00%
Bonds -0.28% -0.39% -0.79% -1.79% 0.67% 1.76% 0.83% 0.00%Cash 0.49% 0.44% 0.65% 1.89% -0.94% -1.89% -0.64% 0.00%Total 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
Change in % Holdings in Economy
Variations on Base Case
No Leverage Wealth Equally Distributed Across Clienteles No Decrease in Risk Tolerance in Crisis Very High Correlations among Asset Class
Returns “Target Weight” Allocation Policy => Naïve
Rebalancing
Variations on Base Case
Base case
BeforeAverage Risk Tol 0.500
US Equity 7.11%
Dev Equity 7.60%Em Equity 9.84%
Bonds 4.71%
Cash 3.00%
Sharpe Ratio 0.274
AfterAverage Risk Tol 0.385
US Equity 13.53%
Dev Equity 13.63%
Em Equity 17.37%
Bonds 6.40%
Cash 1.00%
Sharpe Ratio 0.481
Total Turnover 7.44%
No
Leverage
(A)
0.500
7.20%
7.68%9.93%
4.79%
3.00%
0.280
0.387
14.21%
14.30%
18.03%
7.11%
1.00%
0.513
1.68%
EqualWealth
Clienteles
(B)
0.500
7.23%
7.72%9.96%
4.82%
3.00%
0.282
0.371
14.09%
14.19%
18.08%
6.68%
1.00%
0.503
8.62%
No Decreasein Risk
Tolerance
(C)
0.500
7.11%
7.60%9.84%
4.71%
3.00%
0.274
0.485
10.96%
11.04%
14.01%
5.30%
1.00%
0.382
5.64%
High
Correlations
(D)
0.500
7.11%
7.60%9.84%
4.71%
3.00%
0.274
0.385
16.14%
16.18%
21.22%
8.09%
1.00%
0.533
5.79%
Naïve
Rebalancing
(E)
0.500
7.11%
7.60%9.84%
4.71%
3.00%
0.274
0.385
13.02%
13.11%
16.67%
6.34%
1.00%
0.464
8.23%
Equilibriu
m
Expected
Returns
Equilibriu
m
Expected
Returns
Points of Emphasis
Flight to Quality “Flight to Risk” Optimal Investor Response = f (Risk Tolerance relative to
Average) Turnover: Between 1.5% and 8%, depending on assumptions Extensions:
Liquidity, relative to Average Investment Horizon, relative to Average Taxes, relative to Average
Related Points
Good Companies ≠ Good Investments Low Property Taxes ≠ Low House Prices Publicly Listed Private Equity Firms ≠ “Private
Equity for Everyman”
…..
Popular Sentiment-based Recommendations Generate Some of the Same Actions as Here?
Popular Wisdom: “Be greedy when others are fearful, and fearful when others
are greedy” (Warren Buffet)
Risk premiums are “high” when uncertainty is high (and perhaps liquidity is low), and low when uncertainty is low
“Stocks look attractive when they have been oversold”
Stock prices have decreased ‘a lot’ => risk premiums have increased a lot => stocks are “attractive” (to a risk-tolerant investor)
Black Swans Point 1: Serial Persistence in Stock Market Uncertainty:
Make Decisions using Conditional Variance-Covariance Matrix
Subordinated Stochastic Process Model
Hidden Markov Model
Substantially reduced Black-Swan problem with Conditional Probability Distribution => Provide Simple Illustration
Institutional Risk Management Problem: Better Conditional Probability Model Less Transparent
0
10
20
30
40
50
60
70
80
90
1/2/1990 9/28/1992 6/25/1995 3/21/1998 12/15/2000 9/11/2003 6/7/2006 3/3/2009
VIX Index Level
0
200
400
600
800
1000
1200
1400
1600
1800
1/2/1990 9/28/1992 6/25/1995 3/21/1998 12/15/2000 9/11/2003 6/7/2006 3/3/2009
S&P 500 Index Level
Example: Conditional Variance-Covariance = Control for “Black Swans”
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
1/2/1990 9/28/1992 6/25/1995 3/21/1998 12/15/2000 9/11/2003 6/7/2006 3/3/2009
S&P 500 Returns Scaled by Standard Deviation Measured Over Entire Period
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
1/2/1990 9/28/1992 6/25/1995 3/21/1998 12/15/2000 9/11/2003 6/7/2006 3/3/2009
S&P 500 Returns Scaled by Level of VIX on Preceding Day
Example: Conditional Variance-Covariance = Control for “Black Swans” (cont’d.)
S&P 500 Returns Scaled byStandard Deviation Measured over Entire Period
Mean 0.018302
Median 0.044372
Standard Deviation 1.000000
Sample Variance 1.000000
Kurtosis 11.963779
Skewness -0.200296
Minimum -8.059105
Probability of Seeing Minimum or Less if Normal
0.00000000017166268407%
Maximum 9.325208
Probability of Seeing Maximum or More if Normal
0.00000000000000000000%
S&P 500 Returns Scaled byVIX on Preceding Day
0.017289
0.048046
0.776764
0.603362
4.473268
-0.361824
-5.031819
0.12512451075820100000%
3.307484
91.16557201094780%
Interesting Questions re “Black Swans”?
Who buys insurance against “black swan” events, who supplies this insurance, who self-insures, when does the insurance market “break down”….etc.